Yes, some games can run from external HDDs.
Yes, some games can run from external HDDs.
They can operate from it, though usually you need to set it up at that specific spot. If you place it on one machine and then move the drive elsewhere, it might not function properly because the installer creates files in locations beyond just the drive that are required for use. Of course, there are some exceptions, but this is typically how it goes. If you install it on one machine and then move it to another location where it was previously installed on the same drive, it should work on both devices, even though you only have a single copy of the game files.
This paragraph summarizes the main idea by highlighting a quick takeaway.
For the game to function, a DRM solution such as Steam, UPlay or Origin must be set up beforehand (provided you have the appropriate account). If it uses a different DRM method, installation might not be strictly required.
It should function if you have the appropriate license in your Steam account. You might also need games purchased or downloaded from Gog.com. Usually, additional installations are required for compatibility.
Loading times might be long since drives are generally slow and USB connections aren’t very quick. However, if the game is from Steam or similar platforms and you own it, you should be able to play it. Alternatively, if you have access through a family share or similar arrangement, that should work too.
I conducted some tests with the drives I own. Now I'm uncertain if the external HDD I have spins at 7200rpm or 5400rpm. It supports USB3, but I don't have a 2.5" 7200 HDD for more checks. It's an older 5400rpm SATA1 model. Using CrystalDiskMark, the external HDD performs at speeds similar to SATA2—not extremely fast, but not slow either. Performance with big games will be noticeable. SATA3 offers a 50MB/s boost. An SSD on USB3 is twice as fast as an HDD. (Found some interesting data about the Samsung 840 EVO on SATA3, approaching its theoretical limit...)